Intermediates concentration

Edwards S F 1966 The theory of polymer solutions at intermediate concentration Proc. Phys. See. 88 265... 

Again, Fq. (8.126) describes the situation for known values of z and intermediate concentrations of electrolyte. 

For a single equation, Eqs. (7-36) and (7-37) relate the amounts of the several participants. For multiple reactions, the procedure for finding the concentrations of all participants starts by assuming that the reactions proceed consecutively. Key components are identified. Intermediate concentrations are identified by subscripts. The resulting concentration from a particular reaction is the starting concentration for the next reaction in the series. The final value carries no subscript. After the intermediate concentrations are ehminated algebraically, the compositions of the excess components will be expressible in terms of the key components. 

The unknown intermediate concentration C, has been mathematically ehminated from the last term. In this case, r can be solved for explicitly, but that is not always possible with surface rate equations of greater complexity. The mass transfer coefficient /ci is usually obtainable from correlations. When the experimental data are of (C, r) the other constants can be found by linear plotting. 

Mixed-feed operation is used only for special applications, as when liquor at an intermediate concentration and a certain temperature is desired for additional processing. 

Identification of the intermediates in a multistep reaction is a major objective of studies of reaction mechanisms. When the nature of each intermediate is fairly well understood, a great deal is known about the reaction mechanism. The amount of an intermediate present in a reacting system at any instant of time will depend on the rates of the steps by which it is formed and the rate of its subsequent reaction. A qualitative indication of the relationship between intermediate concentration and the kinetics of the reaction can be gained by considering a simple two-step reaction mechanism ... 

P. G. De Gennes. Exponents for the excluded volume problem as derived by the Wilson method. Phys Lett 38A 339, 1972 J. des Cloiseaux. The Lagrangian theory of polymer solutions at intermediate concentrations. J Phys 26 281-291, 1975. 

The phase-diagram (temperature vs concentration) for a eutectic two-component alloy shows at low temperatures a central two-phase region and two solid one-phase regions at low and high relative concentrations. At the eutectic temperature the liquid phase at an intermediate concentration can all of a sudden coexist with the two solid phases. Upon further increase of temperature, the liquidus lines open up a V-shaped liquid... 

In the preceding subsection we described the preequilibrium assumption. Let us now see how that assumption is related to the steady-state approximation. Scheme XIV will serve for the discussion. The equilibrium and steady-state expressions for the intermediate concentration are... 

Fig. 1. The mixing energies agree rather well with the results of Pasturel et al. and those of Abrikosov et al. . The pair interaction i> (c) is In a very good agreement with the locally relaxed quantity given by Carlsson, and also it is rather similar to the effective pair interaction found by Pasturel et al., although it is smaller approximately by a factor 0.7. The pair interaction u (c) differs from the corresponding quantity reported by Abrikosov et al. , which can be probably attributed to different computational schemes, as we assume neutral spheres, while Abrikosov et al. suppose equal sphere radii. The pair interaction (c) closely follows u (c) for Ni-rich alloys and v (c) for Al-rich alloys, at intermediate concentrations all three quantities...

The formation of PbOj is favoured in solutions containing passivating anions such as SO4 and in chloride solutions of intermediate concentrations very high and very low concentrations of chloride inhibit the formation of Pb02- The platinum/lead bi-electrode performs best in seawater, and is not recommended for use in waters of high resistivity. 

In a subsequent study (S9), isotherms of bromine on pyrolytic graphite showed the presence of several phases C4 Br (n = 2 to 5). X-ray studies confirmed these to be stages 2 to 5, respectively. At intermediate concentrations, X-ray patterns showed mixtures of higher and lower stages. The density and configuration of intercalated bromine molecules were believed to be the same in all stages. Other structural types... 

The product concentration curve shows an inflection point that corresponds with the maximum intermediate concentration. 

The UV-Vis spectral detection of an intermediate in the catalytic reductive alkylation reaction provides only circumstantial evidence of the quinone methide species. If the bioreductive alkylating agent has a 13C label at the methide center, then a 13C-NMR could provide chemical shift evidence of the methide intermediate. Although this concept is simple, the synthesis of such 13C-labeled materials may not be trivial. We carried out the synthesis of the 13C-labeled prekinamycin shown in Scheme 7.5 and prepared its quinone methide by catalytic reduction in an N2 glove box. An enriched 13C-NMR spectrum of this reaction mixture was obtained within 100 min of the catalytic reduction (the time of the peak intermediate concentration in Fig. 7.2). This spectrum clearly shows the chemical shift associated with the quinone methide along with those of decomposition products (Fig. 7.3). 

The effect of concentration can also be complex. For example, the corrosion of mild steel in sulphuric acid, where the rate is unacceptably high in dilute acid and at concentrations above 70 per cent, but is acceptable at intermediate concentrations. 

Interestingly, exceptions are possible. Stewart et al. [81] reported that the effect of magnesium stearate concentration on the dissolution of a model low-dose drug, riboflavin, from capsules was dependent in some manner on the type of filler. Soluble fillers exhibited the anticipated prolonged times with increasing lubricant levels. However, the trends with insoluble fillers were less predictable. In some cases insoluble fillers were only slightly affected by the concentration of magnesium stearate. For others, such as microcrystalline cellulose, there appeared to be an ideal intermediate concentration of lubricant at which the dissolution rate was maximized. 

Since wool is attacked most rapidly by sulphuric acid of intermediate concentration, it is important that drying is carried out either at a relatively low temperature so that reaction of the acid with wool is slow, or very quickly so that the time of exposure of the wool to the critical acid concentrations is brief [146]. Ideally, all the sulphuric acid in the wool is absorbed chemically as bound acid that causes little hydrolytic damage. It is the free acid that can concentrate locally and cause serious degradation. The acid picked up by the vegetable impurities, on the other hand, is free acid that has the desirable effect of beginning the process of attacking the cellulose [286]. 

ILLUSTRATION 4.2 USE OF STEADY-STATE AND PSEUDO EQUILIBRIUM APPROXIMATIONS FOR INTERMEDIATE CONCENTRATIONS... 

Schematic representation of the time dependence of the concentration of the first intermediate in a series of first-order reactions. Initial intermediate concentration is nonzero.

In this case there are two intermediate unspecified reactant concentrations instead of just the single intermediate concentration encountered in Case II. At least one of these concentrations must be determined if one is to be able to appropriately size the reactors. In principle one may follow the procedure used in Case II where the design equations for each CSTR are written and the reactor space times then equated. This procedure gives three equations and three unknowns (VRl9 fBl, and fB2). Thus, for the first reactor,... 

Surhcial stream sediments in the San Francisco estuarine system during 1972 had high residues (350 to 1400 pg/kg DW) at several locations (Phillips and Spies 1988). However, residues were highly variable between sites (Law and Goerlitz 1974). In 1984, low to intermediate concentrations of PCBs (9 to 60 pg/kg DW) were measured at four locations in the San Francisco Bay. Overall, congener profiles resembled Aroclor 1254 and were dominated by pentachlorobiphenyl isomers (NOAA 1987). The patterns of the 11 reported congeners were variable between areas, indicating many sources of different PCB mixtures. 

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